Ropes, Bodies, and Physics

This week, I tried something I'd never done before, but was always interested in doing: rock climbing. Purdue's recreational sports center debuted a new climbing facility last semester, and I finally took the plunge this week and started climbing.

True confessions: first, I'm not very good yet (I've climbed exactly twice!). Second, I'm pretty afraid of heights. (I know, I know! A theatre technician afraid of heights?! I don't like them, but I get over it when I have to for my job.) So all of this is pretty far outside my comfort zone. Maybe that's why I started thinking about the ways climbing overlaps with much of what we do in theatre--as a way to feel less uncomfortable. Regardless of the reason, I have been thinking about what I have been learning in terms of what we do on stage, and I am fascinated by the connections.

My first realization? I've been belaying for years--just not in harness, not with a belay device, and not--obviously--for people. But as I was doing it, I found myself falling into some familiar body-memory motions. The physicality was not terribly different from hoisting or guiding scenery with a bull rope, especially when you holding it in place for a rigger: the rope often goes under your foot, non-dominant hand on the live end of the rope, and dominant on the dead end. Your foot becomes--in some ways--like a belay device, helping to brake the load.

And, of course, there's the rope. We've got our hands on ropes all the time, and I was surprised by how familiar grasping, holding, and pulling that belay rope felt. Ropes have been friends for a long time--the only new information for me was the figure-eight knot; but that came pretty easily--after all, knots have been friends of mine for a long time as well.

Finally, the physics involved is kind of our bread and butter, right? Static loads, dynamic loads, resultant forces along diagonal vectors. I found myself thinking about the differences between keeping my side of the belay rope (as a belayer) mostly vertical vs. moving away from the wall, keeping my side of the rope more at an angle. Basic physics, right? Say the climber is 180#, and is 20 feet in the air. If I'm standing 10' from the wall, the length of my side of the belay rope is going to be the hypotenuse of a right triangle whose legs are 20' and 10', or about 22.4'. The rule of similar triangle tells us that if my climber sits in their harness--i.e., does not impart a dynamic load of any kind, but simple lets the rope hold their weight--their 180# will feel like 201.25# on my side of the belay rope. However, if I move closer to the wall--at a distance of 5'--the load I'll feel will get closer to the weight of the climber: 185#.

Gravity is pulling the belayer straight down; the rope will pull the belayer up but also toward the wall. Indeed, only 180# of force will be pulling up (the forces form the same right triangle as above); only about 90# of force will be pulling the belayer toward the wall. A 180# belayer who can resist 90# of pull toward the wall will be just fine. A 150# belayer, however, would appear to have problems, at least mathematically. So how is it that I can watch belayers that are clearly much lighter than their climbers successfully belay?

The analysis above only deals with a particular moment of time. If we imagine our 180# climber and our 150# belayer (standing 10' from the wall), the analysis is true for the instant the climber rests on the rope. Almost immediately, the belayer will be pulled off the ground and simultaneously swing toward the wall. This swing shortens the length of the belay rope, bringing the load on the belay rope closer to the weight of the climber for every second the belayer is moving closer to the wall, bringing the differential of the load on the ropes closer to the differential of their weight, or 30#.

Okay. So the belayer has swung into the wall, and the differential is only 30#. That should still be enough to lift the belayer off the floor, right? Well, yes. Except for the fact that there's friction in the system. The belay rope passes over a belay bar or other device; because of this, the rope can only travel so fast. The friction may not be large; but even a small decrease in the possible rate of acceleration of the rope reduces the amount of force imparted to the belayer. (A low-friction belay bar would mean that the belayer would, indeed, come up off the ground!)

Obviously, things get more complicated when a climber falls because the dynamic load of the fall imparts a--potentially significantly--higher load on the belay rope. But the basic physics remains the same: we can calculate the load using vector math and similar triangles and (if we knew the coefficient of friction on the belay device) basic principles of friction of a rope around an object. In most cases, if the weight differential between the climber and the belayer isn't significant, everything should work out just fine. :)

Maybe taking your students to a climbing wall to look at the physics of falling wouldn't be a bad idea. I plan to take mine!